Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910180417994752 |
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| author | Biriukov, Yu. A. Morozov, R. D. Dyakonov, I. V. Straupe, S. S. |
| author_facet | Biriukov, Yu. A. Morozov, R. D. Dyakonov, I. V. Straupe, S. S. |
| contents | This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and bioinformatics. We propose two quantum approaches to solve this problem: reduction to Quadratic Unconstrained Binary Optimization (QUBO) and using Grover's quantum search algorithm. For the latter approach, we present an explicit gate-based oracle circuit utilizing Dicke states and Quantum Fourier Transform for edge counting. Numerical simulations demonstrate a quadratic speedup over classical Brute-force search. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27782 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem Biriukov, Yu. A. Morozov, R. D. Dyakonov, I. V. Straupe, S. S. Quantum Physics This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and bioinformatics. We propose two quantum approaches to solve this problem: reduction to Quadratic Unconstrained Binary Optimization (QUBO) and using Grover's quantum search algorithm. For the latter approach, we present an explicit gate-based oracle circuit utilizing Dicke states and Quantum Fourier Transform for edge counting. Numerical simulations demonstrate a quadratic speedup over classical Brute-force search. |
| title | Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.27782 |